The supersymmetric Ward identities on the lattice

Abstract

Supersymmetric (SUSY) Ward identities are considered for the N=1 SU(2) SUSY Yang Mills theory discretized on the lattice with Wilson fermions (gluinos). They are used in order to compute non-perturbatively a subtracted gluino mass and the mixing coefficient of the SUSY current. The computations were performed at gauge coupling β = 2.3 and hopping parameter κ = 0.1925, 0.194, 0.1955 using the two-step multi-bosonic dynamical-fermion algorithm. Our results are consistent with a scenario where the Ward identities are satisfied up to O(a) effects. The vanishing of the gluino mass occurs at a value of the hopping parameter which is not fully consistent with the estimate based on the chiral phase transition. This suggests that, although SUSY restoration appears to occur close to the continuum limit of the lattice theory, the results are still affected by significant systematic effects.

Algorithms for Lattice QCD with Dynamical Fermions

“…The scatter of the points gives a rough indication of the uncertainties in the cost estimates. For the QCD TM fermions there are number of points at the same value for the π mass, because the system shows a first-order phase transition with different costs in each phase [7]. The bands are a subjective extrapolation of the costs.…”

QCD spectroscopy with three light quarks

“…This so-called sign problem may spoil the statistical signal of observables. Experience shows that both situations (with and without sign problem) are possible [13,11]. The sign of the determinant can be controlled by the spectral flow of small eigenvalues.…”

“…A first orientation can be obtained by making a comparison with previous simulations. In [11] TSMB has been used for the N = 1 supersymmetric Yang-Mills theory where the number of flavour is N f = 1 2 . In that simulation condition numbers of O(10 5 ) occurred.…”

Spectrum of SU(2) SUSY Yang-Mills theory with a light gluino

“…P (1) n1 gives a crude estimate of the fermionic measure and is used in the bosonic representation of the determinant. P (2) n2 is a correction factor that is accounted for by a global accept-reject step. The algorithm is made exact by a third polynomial P (3) n3 through reweighting the gauge configurations in the expectation values.…”

“…From the SUSY Ward-identities study [2] it follows κ c (β = 2.3) ≈ 0.197, where κ c (β) is the hopping parameter where the gluino is massless.…”